Bottom Line:
It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise.In addition, its robustness to noise was poorer than that of the Tikhonov filter.Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

Affiliation: Molecular Imaging Program at Stanford (MIPS), Stanford University School of Medicine, Stanford University, Stanford, CA 94305, United States of America.

ABSTRACTIn this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT). We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method's robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM) and contrast-to-noise ratio (CNR) of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov filter. The performance of the Fourier filter was found to be the poorest of all three methods, based on the reconstructed images' lowest resolution (blurriest appearance), generally lowest contrast-to-noise ratio, and lowest robustness to noise. Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

pone.0152597.g012: Robustness to noise of each deconvolution filter, as illustrated for the vessel phantom.σ denotes the standard deviation of the zero-mean Gaussian noise added to the pressure signals, expressed as a percentage of the maximum pressure signal value. Each filter is used at its optimal setting, as determined in the Filter parameter optimization section. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.

Mentions:
In this section, we measure the robustness to noise of each method by adding increasing levels of zero-mean Gaussian noise to the pressure signals. The standard deviation of the noise is expressed as a percentage of the maximum signal amplitude of the original pressure data. Figs 11, 12, 13 and 14 show reconstructions obtained with the three deconvolution methods for different levels of noise. The most obvious effect of the increasing noise levels is to gradually erode the fainter structures in the image; only the brightest features remain visible at the highest noise levels. Figs 11, 12, 13 and 14 also show that the overall CNR of the reconstructions degrades with increasing noise levels. Qualitatively, it can be appreciated that the Tikhonov filter appears to be most robust to the increasing noise levels for all objects. In particular, it visually performs similarly to the Wiener filter for the dot and vessel phantoms, clearly outperforms the Fourier and Wiener filters for the subcutaneous tumor, and arguably performs best for the mouse brain. The performance of the Wiener and Fourier filters, on the other hand, is more variable: the Wiener filter is more robust than the Fourier filter for the dot and vessel phantoms, but the Fourier filter is more robust than the Wiener filter for the subcutaneous tumor and mouse brain scans.

pone.0152597.g012: Robustness to noise of each deconvolution filter, as illustrated for the vessel phantom.σ denotes the standard deviation of the zero-mean Gaussian noise added to the pressure signals, expressed as a percentage of the maximum pressure signal value. Each filter is used at its optimal setting, as determined in the Filter parameter optimization section. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.

Mentions:
In this section, we measure the robustness to noise of each method by adding increasing levels of zero-mean Gaussian noise to the pressure signals. The standard deviation of the noise is expressed as a percentage of the maximum signal amplitude of the original pressure data. Figs 11, 12, 13 and 14 show reconstructions obtained with the three deconvolution methods for different levels of noise. The most obvious effect of the increasing noise levels is to gradually erode the fainter structures in the image; only the brightest features remain visible at the highest noise levels. Figs 11, 12, 13 and 14 also show that the overall CNR of the reconstructions degrades with increasing noise levels. Qualitatively, it can be appreciated that the Tikhonov filter appears to be most robust to the increasing noise levels for all objects. In particular, it visually performs similarly to the Wiener filter for the dot and vessel phantoms, clearly outperforms the Fourier and Wiener filters for the subcutaneous tumor, and arguably performs best for the mouse brain. The performance of the Wiener and Fourier filters, on the other hand, is more variable: the Wiener filter is more robust than the Fourier filter for the dot and vessel phantoms, but the Fourier filter is more robust than the Wiener filter for the subcutaneous tumor and mouse brain scans.

Bottom Line:
It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise.In addition, its robustness to noise was poorer than that of the Tikhonov filter.Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

Affiliation:
Molecular Imaging Program at Stanford (MIPS), Stanford University School of Medicine, Stanford University, Stanford, CA 94305, United States of America.

ABSTRACTIn this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT). We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method's robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM) and contrast-to-noise ratio (CNR) of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov filter. The performance of the Fourier filter was found to be the poorest of all three methods, based on the reconstructed images' lowest resolution (blurriest appearance), generally lowest contrast-to-noise ratio, and lowest robustness to noise. Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.